My oldest is extremely picky and has only ever eaten one vegetable willingly - the potato. I had to get creative in hiding them. This is my homemade sloppy joe recipe which she eats every time and still has no clue about the veggies in the sauce. Using pre-chopped frozen onion or pre-shredded carrots cuts the prep time.
Place red bell pepper, carrots, and onion in a food processor and blend until smooth, scraping down the sides as needed.
Heat a large skillet over medium-high heat. Cook and stir beef in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Stir vegetable mixture into ground beef; cook and stir until heated through, 2 to 3 minutes.
Mix tomato sauce, Worcestershire sauce, ketchup, and molasses into ground beef mixture; cook and stir until heated through and slightly thickened, 5 to 7 minutes. Spread sloppy joe mixture into each bun using a slotted spoon.
If your child is picky about meat also (like mine), you can put some of the sloppy joe in the blender and puree further until it forms a paste and then spread on the bun.
Ground turkey can be used in place of ground beef. Yellow bell pepper can be used in place of red bell pepper.